Ah, another "Christine" eh?
I wish I had the technical knowledge to help.
I have a "Christine" myself. My 01 Cruiser, lots of incidents like this. She'* a 5 speed, so I can't help with the trans diagnosis. Nothing ever has been able to be explained through logic at all. She just randomly goes nuts, then everything is normal. My friends are genuinely afraid of her.
Hope you figure it out! That'* crazy!
If I were you, I would block the wheels and put the parking brake on at all times until you figure out whats going on with the trans. On, off, running or not. Block the wheels just to be on the safe side of things for now.
I would start by checking what Dan said, then I'd personally take it to a trans shop to have them test it, it has to be in the gear selection mechanics somewhere.